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The blind speed sidelobe (BSSL) induced by the ambiguous velocity is a main challenge in the long-time coherent integration based high-speed target detection. In this article, considering the support area difference between the BSSL and the real target, we propose an improved minimized windowed Radon-Fourier transform (RFT)-based radar high-speed target detection method to suppress the BSSL and realize target detection. First, two groups of window functions are designed to force the BSSL support areas to split, and then, minimum operations are adopted to suppress the BSSL. The effect of minimum operation on target detection is theoretically analyzed for the first time. The relationship between detection threshold and false-alarm rate is deduced and an iterative numerical method is designed to determine the threshold. Numerical simulations of the detection performance and BSSL suppression ability are done for the RFT, PRF changing method, complementary window function method (CWFM), and the proposed method, which demonstrates the superiority of the proposed detection method. Finally, the validity of the proposed algorithm is verified by the measured data. Compared with RFT and CWFM, this algorithm can suppress BSSL more significantly.